may be accurately represented. The model is capable of dealing directly 

 with currents and waves, but no reports of such combined wave and 

 current calculations have been published. 



Once any nonlinear effects are included, whether they involve 

 dispersion, dissipation or wave breaking, there is interaction with the 

 current field, and most of the above approaches become inapplicable 

 because Fourier wave components may not be superposed. Boundary 

 conditions around the whole region become important, and it is advisable 

 to solve the differential equations over some spatial grid, using either 

 a finite-difference or finite-element method, even if linear theory is 

 used in part. Noda (1974) used finite differences in his investigation 

 of nearshore circulation. Skovgaard and Jonsson (1976) indicate how 

 finite elements may be used. See Section II, 10. 



8. Small- and Medium-Scale Currents. 



When the length or time scales of a current are comparable with 

 those of waves upon it, it is not appropriate to use refraction theory. 

 The example which has been most studied is the flow caused by a moving 

 ship. This flow interacts with the waves generated by the ship, and 

 work to date has been more successful in showing how difficult the 

 problem is rather than in providing solutions; see Peregrine (Sec. VI, 

 1976). Photographs in Gadd (1975) show just how strong this interaction 

 can be. 



Coastal engineers are more familiar with the case of rip currents. 

 These are often identified visually by the relatively low amplitude of 

 waves advancing toward a beach over a rip current. This low amplitude, 

 as discussed in early papers such as Shepard, et al. (1941), is contrary 

 to what is expected from refraction theory (Arthur, 1950), which is that 

 wave energy would become concentrated over the strongest current. In 

 wave theory terms, this is probably a case where diffraction is 

 important. Other cases in which small-scale currents exist include thin 

 shear layers, e.g., where a current goes straight past a headland, or 

 similar circumstances where a current comes out of an inlet. 

 Photographs in Hales and Herbich (1972) show a jetlike current from an 

 inlet with complex wave formations. 



Theoretical results for small-scale currents are sparse. Evans 

 (1975) successfully modeled deepwater waves incident on a vortex sheet. 

 Except for the reflection, the results for the transmitted waves were 

 very similar to those obtained from refraction theory (Longuet-Higgins 

 and Stewart, 1961) for a slow change of current velocity. McKee (1977) 

 found the reflection coefficient for waves entering a following jet 

 and gave numerical examples for surface waves in deep water. 



Evans' work is extended by Smith (1980) to two vortex sheets 

 modeling a jetlike current. Among the many results presented by Smith 

 there is a tendency for wave amplitudes on the current to be weaker than 

 elsewhere. However, it is worth noting in this context that for waves 



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